Deepa rises her bike at an average speed of 30 km/hr and reaches her destination in 6 hrs . Hema covers the same distance in 4 hrs . If Deepa increases her average speed by 10km/hr and Hema increases her average speed by 5 km/hr , what would be the difference in their time taken to reach the destination ?

Options

A. 54 minutes
B. 1 hour
C. 40 minutes
D. 45 minutes

Explanation

To solve the problem step by step, we will calculate the distance traveled by Deepa, then determine the new speeds for both Deepa and Hema, and finally calculate the time taken by each after the speed increases. Finally, we will find the difference in their times.

### Step 1: Calculate the distance traveled by Deepa
Deepa rides her bike at an average speed of 30 km/hr for 6 hours.

**Distance = Speed × Time**

Distance traveled by Deepa = 30 km/hr × 6 hrs = 180 km

### Step 2: Calculate the new speed of Deepa
Deepa increases her average speed by 10 km/hr.

New speed of Deepa = 30 km/hr + 10 km/hr = 40 km/hr

### Step 3: Calculate the time taken by Deepa at the new speed
Now, we will calculate the time taken by Deepa to cover the same distance (180 km) at her new speed (40 km/hr).

**Time = Distance / Speed**

Time taken by Deepa = 180 km / 40 km/hr = 4.5 hours = 4 hours and 30 minutes

### Step 4: Calculate the new speed of Hema
Hema covers the same distance in 4 hours, so her speed is:

Speed of Hema = Distance / Time = 180 km / 4 hrs = 45 km/hr

Now, Hema increases her speed by 5 km/hr.

New speed of Hema = 45 km/hr + 5 km/hr = 50 km/hr

### Step 5: Calculate the time taken by Hema at the new speed
Now, we will calculate the time taken by Hema to cover the same distance (180 km) at her new speed (50 km/hr).

Time taken by Hema = 180 km / 50 km/hr = 3.6 hours = 3 hours and 36 minutes

### Step 6: Calculate the difference in time taken
Now, we will find the difference in time taken by Deepa and Hema after their speed increases.

Time taken by Deepa = 4 hours 30 minutes = 4.5 hours
Time taken by Hema = 3 hours 36 minutes = 3.6 hours

Difference in time = Time taken by Deepa - Time taken by Hema
Difference = 4.5 hours - 3.6 hours = 0.9 hours = 54 minutes

### Final Answer
The difference in their time taken to reach the destination is **54 minutes**.

---